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Monte-Carlo methods for the pricing of American options: a semilinear BSDE point of view

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  • Bruno Bouchard

    (CEREMADE)

  • Ki Chau

    (CWI)

  • Arij Manai
  • Ahmed Sid-Ali

Abstract

We extend the viscosity solution characterization proved in [5] for call/put American option prices to the case of a general payoff function in a multi-dimensional setting: the price satisfies a semilinear re-action/diffusion type equation. Based on this, we propose two new numerical schemes inspired by the branching processes based algorithm of [8]. Our numerical experiments show that approximating the discontinu-ous driver of the associated reaction/diffusion PDE by local polynomials is not efficient, while a simple randomization procedure provides very good results.

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  • Bruno Bouchard & Ki Chau & Arij Manai & Ahmed Sid-Ali, 2017. "Monte-Carlo methods for the pricing of American options: a semilinear BSDE point of view," Papers 1712.07383, arXiv.org, revised Nov 2018.
    • Handle: RePEc:arx:papers:1712.07383
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    References listed on IDEAS

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    1. Bruno Bouchard & Jean-François Chassagneux, 2016. "Fundamentals and Advanced Techniques in Derivatives Hedging," Post-Print hal-01348864, HAL.
    2. repec:dau:papers:123456789/4273 is not listed on IDEAS
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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